Question

A wheel is at rest. its angular velocity increases uniformly and becomes 80 radians second after 5 seconds. the total angular displacement is:

• A. 800 rad
• B. 400 rad
• C. 200 rad
• D. 100 rad

Answer 1

The correct option is C 200 rad

$w_0=0$ (rest)

w = 80 rad/s

t = 5 second

total angular displacement $0=w_{0}t+\frac{1}{2}\alpha t^2$

or simply given by $w^2=w_0^2+2\alpha \theta$

$\Rightarrow \theta =\frac{w^2-w_0^2}{2\alpha }$; $\alpha =\frac{w-w_0}{t}$

$\alpha =$ angular acceleration

we get $\theta =\frac{{80}^2-0}{2\times \frac{80-0}{5}}$

$\theta =\frac{80\times 5}{2}=200$ radian